In How Children Fail, John Holt describes how very young children approach the world as scientists with enthusiasm for learning. He observes how school teaches children to find the right answer. By fifth grade, school kids can get very good at the “right answer” game and appear successful without real learning.
What is real learning?
The better we understand something, the more places we can use it. He observes that when we teach arithmetic, we teach algebra.
2 somethings plus 3 somethings equals five of those things: 2x + 3x = 5x. When we learn about fractions, we learn that we cannot add unless there is a common denominator. This is true of whole numbers as well.
Without giving the children any preparation, Holt wrote this problem on the blackboard for a first grade class:
2 horses + 3 cows = ?
A number of children gave the answer “five animals,” intuitively discovering a common denominator. Curious about this observation, I gave the problem to my 5 year old son. He also came up with the answer “five animals.”